First - Snuggling vs. Cuddling
Snuggling and cuddling can mean the same thing which is something like "hugging" for comfort or intimacy. But "cuddle" - while it can be mutual - often implies one person cuddling another. That is, there's can be a sense of a "cuddler" giving comfort to a "cuddlee". The following is mostly described as "a father cuddling his baby":
And here, our feline friends "Odin and Ruby are snuggling". Also, Ruby (the cat on the right) is snuggling his nose into Odin's white fur. And just like Ruby, a single person can feel good just "snuggling under the covers". But one could also say, "these cuddling cats are cute".
Now the Answer
Let's assume your scene is a mother talking to her child. The mother is sitting next to her young daughter who is near a doll. The mother is offering some consoling words to the daughter, who is afraid of the dark.
A) "If you're scared, snuggle with that doll, baby." is the most natural of the three you presented. This would be especially true if the doll was rather large and already next to the child. It implies a mutual snuggling, just like Odin and Ruby, above. That would be exactly the correct thing to say to a young child, since the idea of the doll being animate and being able to provide comfort back is what provides comfort to the fearful child.
B) "If you're scared, snuggle that doll, baby." could sound a bit too curt - like an order. However, there's a type of mother-character one might see in movies (or real life I suppose).. the no-fluff, down to earth, common-sense, yet-loving mother that might deliver the message like this.
C) "snuggle up to" focuses more on the movement, and may suggests a more playful action. (Also, between adults, snuggling suggests more intimacy than cuddling.) This would be the least natural, in this case, in my opinion.
The difference between using "snuggle vs. cuddle" with a child would mostly depend on what the child already thinks of as being comforting. It's not the specific word, but rather, which word the child would feel the most comforted by. One could suggest that a child cuddle her doll (like the father above) or cuddle with her doll (like the cats) for comfort, if that's what she is used to doing and calling it.
FYI: This is also reminiscent of the Harlow Monkey Studies.
Google Ngram: snuggle *,cuddle *,snuggle that,snuggle this,snuggle me,cuddle that,cuddle this
Best Answer
The word "race" carries a host of (usually negative) connotations in English as well, and in the wrong situation you can cause a commotion with it. Unfortunately it is the only word we've got that really means what you want.
I'm going to answer this with as little social commentary as possible, but just to be clear, races of humans are not biologically meaningful categories, but ethnicities can be sociologically meaningful.
A race is a distinct group of people, separated from others based on biological factors, usually skin color. It also often corresponds to place of origin or ancestry.
ex: Pacific Islanders or Australian Aborigines are often viewed as belonging to particular races.
An ethnic group or someone's ethnicity is a distinct group of people, separated from others based on sociological or historical factors. It may or may not correspond to race.
ex: Jewish or Hispanic people belong to particular ethnicities, but can be of any race.
If, conversationally, you chose to ask someone about their heritage, it would be safer to ask for their ethnicity than their race, and they would likely give you their race rather than their ethnic group.
However, in your example, worldbuilding, you are defining a group of people by their physical characteristics (and probably also by their social characteristics) so it would be appropriate to call them a race.
ex: In World of Warcraft, the Orcs are a race of green skinned warriors who value bravery in battle.
You would definitely use the word race in this context, as Orcs are a distinct biological population from Trolls or Elves or Humans. It would be trickier if they were all groups of humans who differed only in superficial physical characteristics, but people would be more understanding of the use of race in a completely hypothetical situation like that.